Solving Systems of Equations by Elimination

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does elimination mean in the context of solving systems of equations?

Back

Elimination is a method used to solve systems of equations by removing one variable, allowing for the other variable to be solved easily.

Front

How do you eliminate a variable in a system of equations?

Back

To eliminate a variable, you can add or subtract the equations after multiplying them by suitable coefficients to make the coefficients of one variable the same.

Front

What is the first step in solving a system of equations by elimination?

Back

The first step is to align the equations and decide which variable to eliminate.

Front

If you have the equations 2x + 3y = 6 and 4x + 6y = 12, what can you conclude?

Back

The two equations represent the same line, so there are infinitely many solutions.

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What is the solution to the system of equations 3x + 2y = 12 and 3x - y = 3?

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The solution is (3, 0).

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What does it mean if a system of equations has no solution?

Back

If a system has no solution, it means the lines represented by the equations are parallel and never intersect.

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What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

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How can you check if your solution to a system of equations is correct?

Back

You can check by substituting the solution back into the original equations to see if both equations are satisfied.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines represented by the equations.